<h2>Problem 210</h2>
<div style="color:#666;font-size:80%;">26 September 2008</div><br />
<div class="problem_content">
Consider the set S(r) of points (x,y) with integer coordinates satisfying |x| + |y| <img src='images/symbol_le.gif' width='10' height='12' alt='&le;' border='0' style='vertical-align:middle;' /> r. <br />
Let O be the point (0,0) and C the point (r/4,r/4). <br />
Let N(r) be the number of points B in S(r), so that the triangle OBC has an obtuse angle, i.e. the largest angle &alpha; satisfies 90&deg;<&alpha;<180&deg;.<br />
So, for example, N(4)=24 and N(8)=100.
<p>
What is N(1,000,000,000)?
</p>



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